Kofi Annan has issued a blunt warning that Syria will face a spreading civil war and risk a spillover of the conflict unless Russia, the west and Arab states end their "destructive competition" to force a ceasefire and launch a political process that the opposition insists must see President Bashar al-Assad step down.

In an exclusive interview with the Guardian, the UN envoy called for an end to mutual recriminations and insisted that despite disagreements at an international conference on Syria in Geneva last weekend, the support of the entire UN security council for a political transition in Damascus was a significant achievement that should not be squandered.

"We are trying to implement some of the decisions taken in Geneva, most importantly exploring on the ground the most effective way to stop the violence and get them thinking of the political process," Annan said. "I understand the reaction of the [Syrian] opposition. Maybe in their shoes I would have done the same or gone further because they didn't get 100% of what they wanted. But it doesn't mean they got nothing."

In the face of criticism that his cautious and consensus-building diplomacy is getting nowhere as Syria bleeds – with an estimated 15,000 dead in 16 months – Annan insisted he had no intention of resigning.

The ceasefire, the first point of Annan's six-point plan for Syria, has never been implemented after a brief lull in the first days after it was announced on 12 April, and the country has slipped into a state of all-out war.

The Geneva meeting was intended to "kick-start" the political process, but was overshadowed by a row between Russia and the west over whether Assad must step down before the creation of a transitional government. This crucial issue was fudged to say it could include members of the present government and the opposition "and shall be formed on the basis of mutual consent".

Annan said: "There is a road map so people will know there is an alternative if they stop fighting. What is important is that for the first time the five permanent members [of the security council] came together and agreed on a political transition. They talked about institutions including security sectors and the type of leadership that is required."

But the envoy, also representing the Arab League, made clear that western criticism of Russia, a long-standing ally of Assad, was not enough. "Russia does have influence and can encourage the Syrian government to implement fully the six-point plan and security council resolutions," he said. "But this task cannot be left to the Russians alone. I expect Iran to play a role. Those governments – the US and the Friends of Syria – that have influence with the opposition should also play a role. If they continue with this destructive competition everyone will lose.

"They [the west] accuse the Russians of arming the [Syrian] government. The Russians accuse them of arming the opposition and flooding the place with weapons. This is instead of coming together to see what can be done."

Saudi Arabia and Qatar are financing and arming the Free Syrian Army and the US says it is helping co-ordinate with the rebels and supplying communications equipment.

Hillary Clinton, the US secretary of state, underlined tensions when she told ministers at the Friends of Syria conference in Paris on Friday: "I ask you to reach out to Russia and China and to not only urge but demand that they get off the sidelines and begin to support the legitimate aspirations of the Syrian people."

Annan said he was constrained by his role as mediator and could not speak for the Syrian leader, but added: "Assad has to understand that things cannot continue as they are. I raised the issue of transition in our first meeting in March and nothing has happened to shift people away from the concept of transition. I am sure he realises it has to come."

Critics have made reference to Annan's role as head of UN peacekeeping operations at the time of the Rwandan genocide in 1994 and the massacre of Bosnian Muslims by Serbs at Srebrenica the following year. The implication is that his record makes him the wrong man to be leading negotiations, which – however well-intentioned – provide an excuse for inaction and buying time for the Assad regime to continue the killing.

Annan rejects this charge as unfair. "I am worried about the people of Syria. My only concern is them. If I can help save at least one life I will be happy. I am worried about the alternative that will lead to further militarisation of the conflict.

"I have nothing to prove. As a retiree I could have continued sitting in my garden. But it was difficult to say no when I was approached. When you have been in the game for a while and you have footprints, people will use them for you or against you. When I take a job or decide to resign it is uniquely my decision."